The inner graph \(H\)  in the \(s\) -wide replacement product is chosen to
be a Cayley graph on \(\mathbb {Z}_2^m\)  for some positive integer \(m\) .
Ta-Shma uses the construction of Alon et al. [1]} (AGHP) to
deduce a result similar to lemma:aghp below. To compute the
refined parameter version of our main result theo:main, we will
need the specifics of the AGHP construction.
